# Lipschitz modulus in convex semi-infinite optimization via d.c. functions

María J. Cánovas; Abderrahim Hantoute; Marco A. López; Juan Parra

ESAIM: Control, Optimisation and Calculus of Variations (2008)

- Volume: 15, Issue: 4, page 763-781
- ISSN: 1292-8119

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topCánovas, María J., et al. "Lipschitz modulus in convex semi-infinite optimization via d.c. functions." ESAIM: Control, Optimisation and Calculus of Variations 15.4 (2008): 763-781. <http://eudml.org/doc/90936>.

@article{Cánovas2008,

abstract = {
We are concerned with the Lipschitz modulus of the optimal set mapping
associated with canonically perturbed convex semi-infinite optimization
problems. Specifically, the paper provides a lower and an upper bound for
this modulus, both of them given exclusively in terms of the problem's data.
Moreover, the upper bound is shown to be the exact modulus when the number
of constraints is finite. In the particular case of linear problems the
upper bound (or exact modulus) adopts a notably simplified expression. Our
approach is based on variational techniques applied to certain difference of
convex functions related to the model. Some results of [M.J. Cánovas et al., J. Optim. Theory Appl. (2008) Online First]
(which go back to [M.J. Cánovas, J. Global Optim.41 (2008) 1–13] and [Ioffe, Math. Surveys55 (2000) 501–558; Control Cybern.32 (2003) 543–554])
constitute the starting point of the present work.
},

author = {Cánovas, María J., Hantoute, Abderrahim, López, Marco A., Parra, Juan},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Convex semi-infinite programming; modulus of
metric regularity; d.c. functions; convex semi-infinite programming; modulus of metric regularity},

language = {eng},

month = {7},

number = {4},

pages = {763-781},

publisher = {EDP Sciences},

title = {Lipschitz modulus in convex semi-infinite optimization via d.c. functions},

url = {http://eudml.org/doc/90936},

volume = {15},

year = {2008},

}

TY - JOUR

AU - Cánovas, María J.

AU - Hantoute, Abderrahim

AU - López, Marco A.

AU - Parra, Juan

TI - Lipschitz modulus in convex semi-infinite optimization via d.c. functions

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2008/7//

PB - EDP Sciences

VL - 15

IS - 4

SP - 763

EP - 781

AB -
We are concerned with the Lipschitz modulus of the optimal set mapping
associated with canonically perturbed convex semi-infinite optimization
problems. Specifically, the paper provides a lower and an upper bound for
this modulus, both of them given exclusively in terms of the problem's data.
Moreover, the upper bound is shown to be the exact modulus when the number
of constraints is finite. In the particular case of linear problems the
upper bound (or exact modulus) adopts a notably simplified expression. Our
approach is based on variational techniques applied to certain difference of
convex functions related to the model. Some results of [M.J. Cánovas et al., J. Optim. Theory Appl. (2008) Online First]
(which go back to [M.J. Cánovas, J. Global Optim.41 (2008) 1–13] and [Ioffe, Math. Surveys55 (2000) 501–558; Control Cybern.32 (2003) 543–554])
constitute the starting point of the present work.

LA - eng

KW - Convex semi-infinite programming; modulus of
metric regularity; d.c. functions; convex semi-infinite programming; modulus of metric regularity

UR - http://eudml.org/doc/90936

ER -

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